This paper investigates the relationship between base station (BS) density
and average spectral efficiency (SE) in the downlink of a cellular network.
This relationship has been well known for sparse deployment, i.e. when the
number of BSs is small compared to the number of users. In this case the SE is
independent of BS density. As BS density grows, on the other hand, it has
previously been shown that increasing the BS density increases the SE, but no
tractable form for the SE-BS density relationship has yet been derived. In this
paper we derive such a closed-form result that reveals the SE is asymptotically
a logarithmic function of BS density as the density grows. Further, we study
the impact of this result on the network operator's profit when user demand
varies, and derive the profit maximizing BS density and the optimal amount of
spectrum to be utilized in closed forms. In addition, we provide deployment
planning guidelines that will aid the operator in his decision if he should
invest in densifying his network or in acquiring more spectrum.Comment: This paper will appear in Proc. IEEE Global Commun. Conf. (GLOBECOM)
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